Finite Group Databasebeta

← #13181607

Subgroups — #13181607

Order 1728.

5516 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89076C211yesmaximal, characteristic, complemented
2C2×C3×#3828C211yesmaximal, characteristic, complemented
3C2×C32×#235C211yesmaximal, characteristic, complemented
4#11724611C214yesmaximal, complemented
5#11724581C212yesmaximal, complemented
6#11724580C212yesmaximal, complemented
7#11724579C212yesmaximal, complemented
8#11724578C214yesmaximal, complemented
9C3⋊D3×#235C214yesmaximal, complemented
10D3×#3828C214yesmaximal, complemented
11#11724566C212yesmaximal, complemented
12#11724563C212yesmaximal, complemented
13#11724562C212yesmaximal, complemented
14#10596756—31nomaximal
15#10596669—34nomaximal
16C22×C33×C4C2211yescharacteristic, complemented
17C2×#6312C2212yescomplemented
18#89076C2212yescomplemented
19#89076C2212yescomplemented
20#89076C2212yescomplemented
21#89076C2212yescomplemented
22C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic, complemented
23C2×C4×C3⋊(C3⋊D3)C2212yescomplemented
24C2×#6308C2211yescharacteristic, complemented
25C2×C3×#638C2212yescomplemented
26C3×#3828C2212yescomplemented
27C3×#3828C2212yescomplemented
28C3×#3828C2212yescomplemented
29C3×#3828C2212yescomplemented
30C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
31C2×C3×C4×C3⋊D3C2212yescomplemented
32C2×C3×#634C2211yescharacteristic, complemented
33C2×C32×#67C2212yescomplemented
34C32×#235C2212yescomplemented
35C32×#235C2212yescomplemented
36C32×#235C2212yescomplemented
37C32×#235C2212yescomplemented
38C2×C32×D12C2211yescharacteristic, complemented
39C2×C32×C4×D3C2212yescomplemented
40C2×C32×Dic6C2211yescharacteristic, complemented
41#89039C2218yescomplemented
42C3⋊D3×#67C2218yescomplemented
43D3×#638C2218yescomplemented
44#89031C2218yescomplemented
45#89029C2218yescomplemented
46#89028C2218yescomplemented
47#89026C2214yescomplemented
48C3⋊D3×D12C2214yescomplemented
49D3×C4⋊(C3⋊D3)C2214yescomplemented
50C4×D3×C3⋊D3C2218yescomplemented
51#89022C2214yescomplemented
52#89021C2214yescomplemented
53#89020C2218yescomplemented
54#89019C2214yescomplemented
55#89018C2214yescomplemented
56#89017C2214yescomplemented
57C3⋊D3×Dic6C2214yescomplemented
58#89015C2214yescomplemented
59#89014C2214yescomplemented
60D3×#634C2214yescomplemented
61C2×C32×#41—31no—
62#64367—32no—
63#64367—32no—
64#64366—32no—
65#64366—32no—
66#41×C3⋊D3—34no—
67#41×C3⋊D3—34no—
68#64364—32no—
69#64361—34no—
70#64361—32no—
71C2×#3828—31no—
72C2×#3828—34no—
73C2×#3828—34no—
74C2×#3828—64no—
75C2×#3828D311yescharacteristic, complemented
76C2×C3×#235—34no—
77C2×C3×#235D314yescomplemented
78#64330—316no—
79#64308—38no—
80#64307—38no—
81#64307—38no—
82#64306—316no—
83D3×#235—316no—
84D3×#235—316no—
85#64298—38no—
86#64297—38no—
87#64297—38no—
88C23×C33C2311yescharacteristic
89C22×C3⋊(C3⋊D3)C2312yes—
90C22×C3×C3⋊D3C2312yes—
91C22×C32×D3C2312yes—
92C2×D3×C3⋊D3C2318yes—
93C2×C33×C4C2311yescharacteristic
94C2×C33×C4C2311yescharacteristic
95C2×C33×C4C2311yescharacteristic
96C2×C33×C4C2311yescharacteristic
97C2×C33×C4C2311yescharacteristic
98C2×C33×C4C2311yescharacteristic
99#6312C2314yes—
100#6312C2314yes—
101C2×C3⋊(C3⋊Dic3)C2312yes—
102C4⋊(C3⋊(C3⋊D3))C2312yes—
103C4⋊(C3⋊(C3⋊D3))C2312yes—
104C4×C3⋊(C3⋊D3)C2314yes—
105C4×C3⋊(C3⋊D3)C2314yes—
106#6308C2312yes—
107#6308C2312yes—
108C3×#638C2314yes—
109C3×#638C2314yes—
110C2×C3×C3⋊Dic3C2312yes—
111C3×C4⋊(C3⋊D3)C2312yes—
112C3×C4⋊(C3⋊D3)C2312yes—
113C3×C4×C3⋊D3C2314yes—
114C3×C4×C3⋊D3C2314yes—
115C3×#634C2312yes—
116C3×#634C2312yes—
117C32×#67C2314yes—
118C32×#67C2314yes—
119C2×C32×Dic3C2312yes—
120C32×D12C2312yes—
121C32×D12C2312yes—
122C32×C4×D3C2314yes—
123C32×C4×D3C2314yes—
124C32×Dic6C2312yes—
125C32×Dic6C2312yes—
126#6293C2318yes—
127#6292C2318yes—
128#6291C2318yes—
129#6290C2318yes—
130#6289C2318yes—
131Dic3×C3⋊D3C2318yes—
132D3×C3⋊Dic3C2318yes—
133#5964—94no—
134#5964—91no—
135C32×#41—32no—
136C32×#41—32no—
137C32×#41—32no—
138C32×#41—32no—
139C2×C32×Q8—31no—
140C2×C32×D4—32no—
141C2×C32×D4—31no—
142C22×C32×C4—24no—
143C22×C32×C4—32no—
144C22×C32×C4C2×D314yescomplemented
145C22×C32×C4C2×D311yescharacteristic, complemented
146C2×#638—32no—
147C2×#638—38no—
148C2×#638—38no—
149C2×#638—68no—
150C2×#638C2×D312yescomplemented
151#3832—34no—
152#3832—34no—
153Q8×C3⋊D3—34no—
154Q8×C3⋊D3—34no—
155#3830—38no—
156#3830—38no—
157#3830—34no—
158#3830—34no—
159D4×C3⋊D3—38no—
160D4×C3⋊D3—38no—
161D4×C3⋊D3—34no—
162D4×C3⋊D3—34no—
163#3828—32no—
164#3828—32no—
165#3828—32no—
166#3828—32no—
167#3828—38no—
168#3828—38no—
169#3828—38no—
170#3828—38no—
171#3828—38no—
172#3828—34no—
173#3828—38no—
174#3828—34no—
175#3828—68no—
176#3828—68no—
177#3828—68no—
178#3828—68no—
179#3828C2×D312yescomplemented
180#3828C2×D312yescomplemented
181#3828C2×D312yescomplemented
182#3828C2×D312yescomplemented
183C2×C4⋊(C3⋊D3)—31no—
184C2×C4⋊(C3⋊D3)—34no—
185C2×C4⋊(C3⋊D3)—34no—
186C2×C4⋊(C3⋊D3)—64no—
187C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
188C2×C4×C3⋊D3—32no—
189C2×C4×C3⋊D3—38no—
190C2×C4×C3⋊D3—38no—
191C2×C4×C3⋊D3—68no—
192C2×C4×C3⋊D3C2×D312yescomplemented
193C2×#634—31no—
194C2×#634—34no—
195C2×#634—34no—
196C2×#634—64no—
197C2×#634C2×D311yescharacteristic, complemented
198C2×C3×#67—38no—
199C2×C3×#67C2×D318yescomplemented
200C3×#235—38no—
201C3×#235—38no—
202C3×#235—38no—
203C3×#235—38no—
204C3×#235C2×D318yescomplemented
205C3×#235C2×D318yescomplemented
206C3×#235C2×D318yescomplemented
207C3×#235C2×D318yescomplemented
208C2×C3×D12—34no—
209C2×C3×D12C2×D314yescomplemented
210C2×C3×C4×D3—38no—
211C2×C3×C4×D3C2×D318yescomplemented
212C2×C3×Dic6—34no—
213C2×C3×Dic6C2×D314yescomplemented
214#3811—332no—
215D3×#67—332no—
216D3×#67—332no—
217#3805—332no—
218#3804—332no—
219#3804—332no—
220#3802—316no—
221D3×D12—316no—
222D3×D12—316no—
223C4×D32—332no—
224#3799—316no—
225#3799—316no—
226#3798—332no—
227#3797—316no—
228#3796—316no—
229#3796—316no—
230#3795—316no—
231#3795—316no—
232D3×Dic6—316no—
233D3×Dic6—316no—
234C22×C33—41no—
235C22×C33C2411yescharacteristic
236C22×C33C2411yescharacteristic
237C22×C33C2411yescharacteristic
238C2×C3⋊(C3⋊D3)—42no—
239C2×C3⋊(C3⋊D3)C2414yes—
240C2×C3×C3⋊D3—42no—
241C2×C3×C3⋊D3C2414yes—
242C2×C32×D3—42no—
243C2×C32×D3C2414yes—
244D3×C3⋊D3—48no—
245C33×C4C2411yescharacteristic
246C33×C4C2411yescharacteristic
247C33×C4C2411yescharacteristic
248C33×C4C2411yescharacteristic
249C3⋊(C3⋊Dic3)C2414yes—
250C3×C3⋊Dic3C2414yes—
251C32×Dic3C2414yes—
252C2×C3×#41—34no—
253C2×C3×#41—91no—
254#1010—98no—
255#1010—98no—
256#1010—92no—
257#1010—92no—
258#1009—98no—
259#1009—98no—
260#1009—92no—
261#1009—92no—
262D3×#41—916no—
263D3×#41—916no—
264D3×#41—94no—
265D3×#41—94no—
266#1007—98no—
267#1007—92no—
268#1004—98no—
269#1004—916no—
270#1004—94no—
271#1004—92no—
272C2×#235—34no—
273C2×#235—916no—
274C2×#235—94no—
275C2×#235—91no—
276C2×#235—94no—
277C2×#235—184no—
278C2×#235C3⋊D311yescharacteristic, complemented
279C23×C32—24no—
280C23×C32—32no—
281C23×C32C22×D314yes—
282C23×C32C22×D311yescharacteristic
283C22×C3⋊D3—32no—
284C22×C3⋊D3—38no—
285C22×C3⋊D3—38no—
286C22×C3⋊D3—68no—
287C22×C3⋊D3C22×D312yes—
288C22×C3×D3—38no—
289C22×C3×D3C22×D318yes—
290C2×D32—332no—
291C32×Q8—32no—
292C32×Q8—32no—
293C32×D4—34no—
294C32×D4—34no—
295C32×D4—32no—
296C32×D4—32no—
297C2×C32×C4—24no—
298C2×C32×C4—24no—
299C2×C32×C4—24no—
300C2×C32×C4—24no—
301C2×C32×C4—24no—
302C2×C32×C4—24no—
303C2×C32×C4—32no—
304C2×C32×C4—34no—
305C2×C32×C4—34no—
306C2×C32×C4C22×D314yes—
307C2×C32×C4C22×D314yes—
308C2×C32×C4C22×D314yes—
309C2×C32×C4C22×D314yes—
310C2×C32×C4C22×D314yes—
311C2×C32×C4C22×D314yes—
312C2×C32×C4C22×D311yescharacteristic
313C2×C32×C4C22×D311yescharacteristic
314C2×C32×C4C22×D311yescharacteristic
315C2×C32×C4C22×D311yescharacteristic
316C2×C32×C4C22×D311yescharacteristic
317C2×C32×C4C22×D311yescharacteristic
318#638—34no—
319#638—34no—
320#638—38no—
321#638—38no—
322#638—316no—
323#638—316no—
324#638—616no—
325#638—616no—
326#638C22×D314yes—
327#638C22×D314yes—
328C2×C3⋊Dic3—32no—
329C2×C3⋊Dic3—38no—
330C2×C3⋊Dic3—38no—
331C2×C3⋊Dic3—68no—
332C2×C3⋊Dic3C22×D312yes—
333C4⋊(C3⋊D3)—38no—
334C4⋊(C3⋊D3)—32no—
335C4⋊(C3⋊D3)—32no—
336C4⋊(C3⋊D3)—38no—
337C4⋊(C3⋊D3)—38no—
338C4⋊(C3⋊D3)—68no—
339C4⋊(C3⋊D3)—68no—
340C4⋊(C3⋊D3)C22×D312yes—
341C4⋊(C3⋊D3)C22×D312yes—
342C4×C3⋊D3—38no—
343C4×C3⋊D3—34no—
344C4×C3⋊D3—34no—
345C4×C3⋊D3—38no—
346C4×C3⋊D3—316no—
347C4×C3⋊D3—316no—
348C4×C3⋊D3—616no—
349C4×C3⋊D3—616no—
350C4×C3⋊D3C22×D314yes—
351C4×C3⋊D3C22×D314yes—
352#634—32no—
353#634—32no—
354#634—38no—
355#634—38no—
356#634—38no—
357#634—68no—
358#634—68no—
359#634C22×D312yes—
360#634C22×D312yes—
361C3×#67—316no—
362C3×#67—316no—
363C3×#67C22×D3116yes—
364C3×#67C22×D3116yes—
365C2×C3×Dic3—38no—
366C2×C3×Dic3C22×D318yes—
367C3×D12—38no—
368C3×D12—38no—
369C3×D12C22×D318yes—
370C3×D12C22×D318yes—
371C3×C4×D3—316no—
372C3×C4×D3—316no—
373C3×C4×D3C22×D3116yes—
374C3×C4×D3C22×D3116yes—
375C3×Dic6—38no—
376C3×Dic6—38no—
377C3×Dic6C22×D318yes—
378C3×Dic6C22×D318yes—
379#627—332no—
380#626—332no—
381#626—332no—
382#625—332no—
383#624—332no—
384D3×Dic3—332no—
385D3×Dic3—332no—
386#585—271noSylow
387C2×C33—21no—
388C2×C33—21no—
389C2×C33—21no—
390C2×C33C2511yescharacteristic
391C3⋊(C3⋊D3)—24no—
392C3×C3⋊D3—24no—
393C32×D3—24no—
394C3×#41—38no—
395C3×#41—38no—
396C3×#41—38no—
397C3×#41—38no—
398C3×#41—92no—
399C3×#41—92no—
400C3×#41—92no—
401C3×#41—92no—
402C2×C3×Q8—34no—
403C2×C3×Q8—91no—
404C2×C3×D4—38no—
405C2×C3×D4—34no—
406C2×C3×D4—92no—
407C2×C3×D4—91no—
408C22×C3×C4—24no—
409C22×C3×C4—38no—
410C22×C3×C4—92no—
411C22×C3×C4D3214yescomplemented
412C22×C3×C4C2×C3⋊D311yescharacteristic, complemented
413C2×#67—38no—
414C2×#67—932no—
415C2×#67—98no—
416C2×#67—92no—
417C2×#67—98no—
418C2×#67—188no—
419C2×#67C2×C3⋊D312yescomplemented
420#239—916no—
421#239—916no—
422#239—94no—
423#239—94no—
424D3×Q8—916no—
425D3×Q8—916no—
426D3×Q8—94no—
427D3×Q8—94no—
428#237—916no—
429#237—916no—
430#237—932no—
431#237—932no—
432#237—98no—
433#237—98no—
434#237—94no—
435#237—94no—
436D3×D4—916no—
437D3×D4—916no—
438D3×D4—932no—
439D3×D4—932no—
440D3×D4—98no—
441D3×D4—98no—
442D3×D4—94no—
443D3×D4—94no—
444#235—38no—
445#235—38no—
446#235—38no—
447#235—38no—
448#235—916no—
449#235—932no—
450#235—916no—
451#235—932no—
452#235—98no—
453#235—98no—
454#235—98no—
455#235—98no—
456#235—92no—
457#235—92no—
458#235—92no—
459#235—92no—
460#235—98no—
461#235—94no—
462#235—98no—
463#235—94no—
464#235—188no—
465#235—188no—
466#235—188no—
467#235—188no—
468#235C2×C3⋊D312yescomplemented
469#235C2×C3⋊D312yescomplemented
470#235C2×C3⋊D312yescomplemented
471#235C2×C3⋊D312yescomplemented
472C2×D12—34no—
473C2×D12—916no—
474C2×D12—94no—
475C2×D12—91no—
476C2×D12—94no—
477C2×D12—184no—
478C2×D12C2×C3⋊D311yescharacteristic, complemented
479C2×C4×D3—38no—
480C2×C4×D3—932no—
481C2×C4×D3—98no—
482C2×C4×D3—92no—
483C2×C4×D3—98no—
484C2×C4×D3—188no—
485C2×C4×D3C2×C3⋊D312yescomplemented
486C2×Dic6—34no—
487C2×Dic6—916no—
488C2×Dic6—94no—
489C2×Dic6—91no—
490C2×Dic6—94no—
491C2×Dic6—184no—
492C2×Dic6C2×C3⋊D311yescharacteristic, complemented
493C22×C32—24no—
494C22×C32—24no—
495C22×C32—24no—
496C22×C32—34no—
497C22×C32—41no—
498C22×C32—44no—
499C22×C32—48no—
500C22×C32—122no—
501C22×C32C23×D314yes—
502C22×C32C23×D314yes—
503C22×C32C23×D314yes—
504C22×C32C23×D311yescharacteristic
505C22×C32C23×D311yescharacteristic
506C22×C32C23×D311yescharacteristic
507C2×C3⋊D3—34no—
508C2×C3⋊D3—316no—
509C2×C3⋊D3—42no—
510C2×C3⋊D3—616no—
511C2×C3⋊D3—128no—
512C2×C3⋊D3—122no—
513C2×C3⋊D3—128no—
514C2×C3⋊D3—1216no—
515C2×C3⋊D3C23×D314yes—
516C2×C3×D3—316no—
517C2×C3×D3—48no—
518C2×C3×D3—128no—
519C2×C3×D3C23×D3116yes—
520D32—1232no—
521C32×C4—24no—
522C32×C4—24no—
523C32×C4—24no—
524C32×C4—24no—
525C32×C4—34no—
526C32×C4C23×D314yes—
527C32×C4C23×D314yes—
528C32×C4C23×D314yes—
529C32×C4C23×D314yes—
530C32×C4C23×D311yescharacteristic
531C32×C4C23×D311yescharacteristic
532C32×C4C23×D311yescharacteristic
533C32×C4C23×D311yescharacteristic
534C3⋊Dic3—34no—
535C3⋊Dic3—316no—
536C3⋊Dic3—616no—
537C3⋊Dic3C23×D314yes—
538C3×Dic3—316no—
539C3×Dic3C23×D3116yes—
5402−1+4—272no—
5412−1+4—272no—
5422−1+4—272no—
543H(5,𝔽2)—274no—
544H(5,𝔽2)—272no—
545H(5,𝔽2)—272no—
546H(5,𝔽2)—272no—
547C2×#41—31no—
548C2×#41—91no—
549C2×#41—274no—
550C2×#41—274no—
551C2×#41—274no—
552C2×#41—271no—
553C33#58511yescharacteristic, complemented, Sylow
554C23×C3—24no—
555C23×C3—38no—
556C23×C3—92no—
557C23×C3C2×D3214yes—
558C23×C3C22×C3⋊D311yescharacteristic
559C22×D3—38no—
560C22×D3—932no—
561C22×D3—98no—
562C22×D3—92no—
563C22×D3—98no—
564C22×D3—188no—
565C22×D3C22×C3⋊D312yes—
566C3×Q8—38no—
567C3×Q8—38no—
568C3×Q8—92no—
569C3×Q8—92no—
570C3×D4—316no—
571C3×D4—316no—
572C3×D4—38no—
573C3×D4—38no—
574C3×D4—94no—
575C3×D4—94no—
576C3×D4—92no—
577C3×D4—92no—
578C2×C3×C4—24no—
579C2×C3×C4—24no—
580C2×C3×C4—24no—
581C2×C3×C4—24no—
582C2×C3×C4—24no—
583C2×C3×C4—24no—
584C2×C3×C4—38no—
585C2×C3×C4—316no—
586C2×C3×C4—316no—
587C2×C3×C4—92no—
588C2×C3×C4—94no—
589C2×C3×C4—94no—
590C2×C3×C4C2×D3214yes—
591C2×C3×C4C2×D3214yes—
592C2×C3×C4C2×D3214yes—
593C2×C3×C4C2×D3214yes—
594C2×C3×C4C2×D3214yes—
595C2×C3×C4C2×D3214yes—
596C2×C3×C4C22×C3⋊D311yescharacteristic
597C2×C3×C4C22×C3⋊D311yescharacteristic
598C2×C3×C4C22×C3⋊D311yescharacteristic
599C2×C3×C4C22×C3⋊D311yescharacteristic
600C2×C3×C4C22×C3⋊D311yescharacteristic
601C2×C3×C4C22×C3⋊D311yescharacteristic
602#67—316no—
603#67—316no—
604#67—932no—
605#67—932no—
606#67—916no—
607#67—916no—
608#67—94no—
609#67—94no—
610#67—98no—
611#67—98no—
612#67—1816no—
613#67—1816no—
614#67C22×C3⋊D314yes—
615#67C22×C3⋊D314yes—
616C2×Dic3—38no—
617C2×Dic3—932no—
618C2×Dic3—98no—
619C2×Dic3—92no—
620C2×Dic3—98no—
621C2×Dic3—188no—
622C2×Dic3C22×C3⋊D312yes—
623D12—38no—
624D12—38no—
625D12—932no—
626D12—98no—
627D12—98no—
628D12—98no—
629D12—92no—
630D12—92no—
631D12—188no—
632D12—188no—
633D12C22×C3⋊D312yes—
634D12C22×C3⋊D312yes—
635C4×D3—316no—
636C4×D3—316no—
637C4×D3—932no—
638C4×D3—932no—
639C4×D3—98no—
640C4×D3—916no—
641C4×D3—916no—
642C4×D3—94no—
643C4×D3—94no—
644C4×D3—98no—
645C4×D3—1816no—
646C4×D3—1816no—
647C4×D3C22×C3⋊D314yes—
648C4×D3C22×C3⋊D314yes—
649Dic6—38no—
650Dic6—38no—
651Dic6—932no—
652Dic6—98no—
653Dic6—98no—
654Dic6—92no—
655Dic6—92no—
656Dic6—98no—
657Dic6—188no—
658Dic6—188no—
659Dic6C22×C3⋊D312yes—
660Dic6C22×C3⋊D312yes—
661C2×C32—28no—
662C2×C32—21no—
663C2×C32—24no—
664C2×C32—21no—
665C2×C32—21no—
666C2×C32—24no—
667C2×C32—24no—
668C2×C32—24no—
669C2×C32—44no—
670C2×C32—44no—
671C2×C32—64no—
672C2×C32C24×D314yes—
673C2×C32C24×D311yescharacteristic
674C3⋊D3—24no—
675C3⋊D3—64no—
676C3⋊D3—616no—
677C3⋊D3—1216no—
678C3×D3—216no—
679C3×D3—616no—
680#41—32no—
681#41—32no—
682#41—32no—
683#41—32no—
684#41—92no—
685#41—92no—
686#41—92no—
687#41—92no—
688#41—278no—
689#41—278no—
690#41—274no—
691#41—274no—
692#41—278no—
693#41—274no—
694#41—274no—
695#41—278no—
696#41—274no—
697#41—274no—
698#41—272no—
699#41—272no—
700#41—272no—
701#41—272no—
702C2×Q8—31no—
703C2×Q8—91no—
704C2×Q8—274no—
705C2×Q8—274no—
706C2×Q8—274no—
707C2×Q8—271no—
708C2×D4—32no—
709C2×D4—31no—
710C2×D4—92no—
711C2×D4—91no—
712C2×D4—274no—
713C2×D4—274no—
714C2×D4—278no—
715C2×D4—274no—
716C2×D4—278no—
717C2×D4—278no—
718C2×D4—272no—
719C2×D4—271no—
720C22×C4—32no—
721C22×C4—92no—
722C22×C4—278no—
723C22×C4—272no—
724C22×C4D3×C3⋊D311yescharacteristic, complemented
725C22×C3—24no—
726C22×C3—24no—
727C22×C3—24no—
728C22×C3—316no—
729C22×C3—44no—
730C22×C3—41no—
731C22×C3—48no—
732C22×C3—94no—
733C22×C3—128no—
734C22×C3—362no—
735C22×C3C22×D3214yes—
736C22×C3C22×D3214yes—
737C22×C3C22×D3214yes—
738C22×C3C23×C3⋊D311yescharacteristic
739C22×C3C23×C3⋊D311yescharacteristic
740C22×C3C23×C3⋊D311yescharacteristic
741C2×D3—316no—
742C2×D3—42no—
743C2×D3—916no—
744C2×D3—94no—
745C2×D3—128no—
746C2×D3—1816no—
747C2×D3—368no—
748C2×D3—3632no—
749C2×D3—368no—
750C2×D3—362no—
751C2×D3—3616no—
752C2×D3C23×C3⋊D314yes—
753C3×C4—24no—
754C3×C4—24no—
755C3×C4—24no—
756C3×C4—24no—
757C3×C4—316no—
758C3×C4—94no—
759C3×C4C22×D3214yes—
760C3×C4C22×D3214yes—
761C3×C4C22×D3214yes—
762C3×C4C22×D3214yes—
763C3×C4C23×C3⋊D311yescharacteristic
764C3×C4C23×C3⋊D311yescharacteristic
765C3×C4C23×C3⋊D311yescharacteristic
766C3×C4C23×C3⋊D311yescharacteristic
767Dic3—316no—
768Dic3—916no—
769Dic3—94no—
770Dic3—1816no—
771Dic3C23×C3⋊D314yes—
772C32—24no—
773C32#596414yescomplemented
774C32#596411yescharacteristic, complemented
775C23—32no—
776C23—92no—
777C23—278no—
778C23—272no—
779C23C2×D3×C3⋊D311yescharacteristic
780Q8—32no—
781Q8—32no—
782Q8—92no—
783Q8—92no—
784Q8—278no—
785Q8—272no—
786Q8—272no—
787D4—34no—
788D4—34no—
789D4—32no—
790D4—32no—
791D4—94no—
792D4—94no—
793D4—92no—
794D4—92no—
795D4—278no—
796D4—278no—
797D4—278no—
798D4—274no—
799D4—274no—
800D4—272no—
801D4—272no—
802C2×C4—32no—
803C2×C4—34no—
804C2×C4—34no—
805C2×C4—92no—
806C2×C4—94no—
807C2×C4—94no—
808C2×C4—278no—
809C2×C4—278no—
810C2×C4—278no—
811C2×C4—272no—
812C2×C4—274no—
813C2×C4—274no—
814C2×C4C2×D3×C3⋊D311yescharacteristic
815C2×C4C2×D3×C3⋊D311yescharacteristic
816C2×C4C2×D3×C3⋊D311yescharacteristic
817C2×C4C2×D3×C3⋊D311yescharacteristic
818C2×C4C2×D3×C3⋊D311yescharacteristic
819C2×C4C2×D3×C3⋊D311yescharacteristic
820C2×C3—28no—
821C2×C3—24no—
822C2×C3—24no—
823C2×C3—24no—
824C2×C3—21no—
825C2×C3—21no—
826C2×C3—21no—
827C2×C3—24no—
828C2×C3—44no—
829C2×C3—44no—
830C2×C3—616no—
831C2×C3—184no—
832C2×C3C23×D3214yes—
833C2×C3C24×C3⋊D311yescharacteristic
834D3—24no—
835D3—616no—
836D3—1816no—
837D3—184no—
838D3—3616no—
839C22—34no—
840C22—41no—
841C22—94no—
842C22—122no—
843C22—274no—
844C22—362no—
845C22—1082no—
846C22—1088no—
847C22C22×D3×C3⋊D311yescharacteristic
848C22C22×D3×C3⋊D311yescharacteristic
849C22C22×D3×C3⋊D311yescharacteristic
850C4—34no—
851C4—94no—
852C4—274no—
853C4C22×D3×C3⋊D311yescharacteristic
854C4C22×D3×C3⋊D311yescharacteristic
855C4C22×D3×C3⋊D311yescharacteristic
856C4C22×D3×C3⋊D311yescharacteristic
857C3—24no—
858C3#1059666914yescomplemented
859C3#1059675611yescharacteristic, complemented
860C2—21no—
861C2—21no—
862C2—21no—
863C2—64no—
864C2—184no—
865C2—544no—
866C2C23×D3×C3⋊D311yescharacteristic
subgroupG/H
centerC4C22×D3×C3⋊D3
commutator, socle, cosocleC2×C33C25
FrattiniC2C23×D3×C3⋊D3
FittingC22×C33×C4C22
hypercenterC22×C4D3×C3⋊D3
hypocenterC33#585
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C4 ◁ C22×C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#89076C2semidirect
2. C2×C3×#3828C2semidirect
3. C2×C32×#235C2semidirect
4. #11724611C2semidirect
5. #11724581C2semidirect
6. #11724580C2semidirect
7. #11724579C2semidirect
8. #11724578C2semidirect
9. C3⋊D3×#235C2semidirect
10. D3×#3828C2semidirect
11. #11724566C2semidirect
12. #11724563C2semidirect
13. #11724562C2semidirect
16. C22×C33×C4C22semidirect
17. C2×#6312C22semidirect
18. #89076C22semidirect
19. #89076C22semidirect
20. #89076C22semidirect
21. #89076C22semidirect
22. C2×C4⋊(C3⋊(C3⋊D3))C22semidirect
23. C2×C4×C3⋊(C3⋊D3)C22semidirect
24. C2×#6308C22semidirect
25. C2×C3×#638C22semidirect
26. C3×#3828C22semidirect
27. C3×#3828C22semidirect
28. C3×#3828C22semidirect
29. C3×#3828C22semidirect
30. C2×C3×C4⋊(C3⋊D3)C22semidirect
31. C2×C3×C4×C3⋊D3C22semidirect
32. C2×C3×#634C22semidirect
33. C2×C32×#67C22semidirect
34. C32×#235C22semidirect
35. C32×#235C22semidirect
36. C32×#235C22semidirect
37. C32×#235C22semidirect
38. C2×C32×D12C22semidirect
39. C2×C32×C4×D3C22semidirect
40. C2×C32×Dic6C22semidirect
41. #89039C22semidirect
42. C3⋊D3×#67C22semidirect
43. D3×#638C22semidirect
44. #89031C22semidirect
45. #89029C22semidirect
46. #89028C22semidirect
47. #89026C22semidirect
48. C3⋊D3×D12C22semidirect
49. D3×C4⋊(C3⋊D3)C22semidirect
50. C4×D3×C3⋊D3C22semidirect
51. #89022C22semidirect
52. #89021C22semidirect
53. #89020C22semidirect
54. #89019C22semidirect
55. #89018C22semidirect
56. #89017C22semidirect
57. C3⋊D3×Dic6C22semidirect
58. #89015C22semidirect
59. #89014C22semidirect
60. D3×#634C22semidirect
75. C2×#3828D3semidirect
77. C2×C3×#235D3semidirect
144. C22×C32×C4C2×D3semidirect
145. C22×C32×C4C2×D3semidirect
150. C2×#638C2×D3semidirect
179. #3828C2×D3semidirect
180. #3828C2×D3semidirect
181. #3828C2×D3semidirect
182. #3828C2×D3semidirect
187. C2×C4⋊(C3⋊D3)C2×D3semidirect
192. C2×C4×C3⋊D3C2×D3semidirect
197. C2×#634C2×D3semidirect
199. C2×C3×#67C2×D3semidirect
204. C3×#235C2×D3semidirect
205. C3×#235C2×D3semidirect
206. C3×#235C2×D3semidirect
207. C3×#235C2×D3semidirect
209. C2×C3×D12C2×D3semidirect
211. C2×C3×C4×D3C2×D3semidirect
213. C2×C3×Dic6C2×D3semidirect
278. C2×#235C3⋊D3semidirect
411. C22×C3×C4D32semidirect
412. C22×C3×C4C2×C3⋊D3semidirect
419. C2×#67C2×C3⋊D3semidirect
468. #235C2×C3⋊D3semidirect
469. #235C2×C3⋊D3semidirect
470. #235C2×C3⋊D3semidirect
471. #235C2×C3⋊D3semidirect
478. C2×D12C2×C3⋊D3semidirect
485. C2×C4×D3C2×C3⋊D3semidirect
492. C2×Dic6C2×C3⋊D3semidirect
553. C33#585semidirect
724. C22×C4D3×C3⋊D3semidirect
773. C32#5964semidirect
774. C32#5964semidirect
858. C3#10596669semidirect
859. C3#10596756semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#890762
C2×C3×#38282
C2×C32×#2352
#117246112
#117245812
#117245802
#117245792
#117245782
C3⋊D3×#2352
D3×#38282
#117245662
#117245632
#117245622
#105967563
#105966693